How to make image same shape as another image

The cleanest, highest resolution way is to draw the graphics using the (vector) shape tools so that they will always render at the current resolution of the document even if resized; then stack and mask the layers appropriately. These are the steps shown in the demo below:

1. Draw the two rectangles as vector shape layers, and stack them behind the image layer. I grouped the rectangles, but you don’t have to. 

2. With the Rectangle tool set to Path mode, draw a rectangle shape over the image. 

3. On the new rectangle path, drag the rounded corner widgets until the end is fully rounded (half circle). 

4. With that rectangle path selected in the Paths panel, choose Layer > Vector Mask > Current Path. It does what it says: Creates a vector mask from the currently selected path. The image is now masked by that path. 

5. If you need to recompose the image within the vector mask, unlink the mask from the image, then drag the image. 

6. If needed, trim the transparent area outside the blue and white rectangles by choosing Image > Trim.

The final exported smoothness of the edges will depend on the pixel dimensions of the document and exported copy; larger (higher resolution) is smoother.